Question

if x is equal to 3 + 2 root 2 find the value of x square + 1 upon x square​

Answer 1

...............................

Answer 2

# Solution -

According to the Question:

➟ x = 3 + 2√2 , then,

➟ 1/x = 1/3 + 2√2

On rationalising, we get :-

➟ 1/3 + 2√2 × 3 - 2√2/ 3 - 2 √2

➟ 3 - 2√2 / (3)² - (2√2)²

➟ 3 - 2√2 / 9 - 8

➟ 3 - 2√2

Now,

➟ ( x + 1/x )² = x² + 1/x² + 2 × x × 1/x

➟ (3 + 2√2 + 3 - 2√2)² = x² + 1/x² + 2

➟ (3 + 3)² = x² + 1/x² + 2

➟ (6)² - 2 = x² + 1/x²

➟ 36 - 2 = x² + 1/x²

➟ 34 = x² + 1/x²

∴ x² + 1/x² = 34 ____________[ANSWER]